Clean water and sanitation are major global challenges highlighted by the UN Sustainable Development Goals. Water treatment using energy-efficient membrane technologies is one of the most promising solutions. Despite decades of research, the membrane permeability-selectivity trade-off remains the major challenge for synthetic membranes. To overcome this challenge, here we develop a two-dimensional cobalt-functionalized vermiculite membrane (Co@VMT), which innovatively combines the properties of membrane filtration and nanoconfinement catalysis. The Co@VMT membrane demonstrates a high water permeance of 122.4 L·m−2·h−1·bar−1, which is two orders of magnitude higher than that of the VMT membrane (1.1 L·m−2·h−1·bar−1). Moreover, the Co@VMT membrane is applied as a nanofluidic advanced oxidation process platform to activate peroxymonosulfate (PMS) for degradation of several organic pollutants (dyes, pharmaceuticals, and phenols) and shows excellent degradation performance (~100%) and stability (for over 107 h) even in real-world water matrices. Importantly, safe and non-toxic effluent water quality is ensured by the Co@VMT membrane/PMS system without brine, which is totally different from the molecular sieving-based VMT membrane with the concentrated pollutants remaining in the brine. This work can serve as a generic design blueprint for the development of diverse nanofluidic catalytic membranes to overcome the persistent membrane permeability-selectivity issue in water purification.